Paul Penfield, Jr.

Paul Penfield, Jr., is Professor of Electrical Engineering, Emeritus, in the Department of Electrical Engineering and Computer Science at MIT.

  • Tellegen's Theorem and Electrical Networks

    Paul Penfield, Jr., Robert Spencer, and S. Duinker

    B. D. H. Tellegen was the first to point out (1952, 1953) the generality and wide-ranging usefulness of the theorem that bears his name. Nevertheless, the theorem is still not as widely known as its utility warrants. The authors of this monograph set out to correct this neglect, noting that “There is hardly a basic network theorem that cannot be proved by invoking Tellegen's theorem. The simplicity and generality of the theorem make it attractive pedagogically, and its ability to generalize known results and lead to new results indicates its research value. This theorem definitely should be in every circuit designer's kit of tools.”

    Tellegen's theorem is unusual in that it depends solely upon Kirchhoff's laws and the topology of the network. The theorem thus applies to all electrical networks that obey Kirchhoff's laws, whether linear or nonlinear, time-invariant or time-variant, reciprocal or nonreciprocal, passive or active, single-valued or multiple-valued, hysterectic or nonhysteretic. The excitation is arbitrary – it may be sinusoidal, exponential, periodic, transient, or random. Also, the initial conditions may be arbitrarily chosen. The modern interest in nonlinear and time-variant networks gives Tellegen's theorem a special new importance, because it is one of the very few general theorems that apply to such networks.

    To demonstrate its range of applications and the theorem's great power in the derivation of other basic and important theorems about electrical networks (and the extent that these other theorems are special cases of Tellegen's), the authors have collected more than 100 such theorems and have shown that they can be proved from Tellegen's theorem. Most of these were known before; but some are extended in their range of validity, and a few are new. (Apart from Tellegen's theorem, this collection of theorems is valuable in its own right.) Applications are given to automated network synthesis and to nonlinear, time-varying, switching, nonreciprocal, and other networks – all the major areas of network theory are covered. In addition, extensions of the theorem to other physical systems are discussed, including applications to the electromagnetic field, electron beams and plasmas, and quantum mechanics.

    The theorem is proved in its most general form thus far known. In addition, two weaker forms that have useful properties for certain applications are presented. In these weaker forms, the theorem applies to voltages, currents, and wave (or scattering) variables. The use of wave variables in Tellegen's theorem is believed to be new.

    • Hardcover $10.00
  • Electrodynamics of Moving Media

    Paul Penfield, Jr. and Hermann A. Haus

    For more than fifty years there has been a controversy about the correctness of several apparently different electrodynamic formulations for moving media. The research reported here has resolved this controversy.

    In 1908 H. Minkowski proposed his formulation, in which Maxwell's equations have the same form as for stationary media. Later, the formulation of M. Abraham appeared, with a different expression for electromagnetic momentum and, therefore, small relativistic differences in the force predicted. About ten years ago, L. J. Chu developed a new formulation, with significant nonrelativistic differences in the force. Chu's formulation has several advantages, including simplicity, ease of learning, and especially its simple model for magnetization. But before this or any other formulation could be taught or used with confidence, the question of the different force distributions had to be resolved.

    Experiments have not been successful in resolving the controversy because many of the differences concern small relativistic effects. The resolution had to come from more complete theoretical understanding. The authors have found that none of the force expressions “is complete; each must be modified, and when so modified all are in agreement.”

    The authors were led to this conclusion by carefully identifying the energies and powers, and by establishing a law of conservation of energy consistent with thermodynamics, continuum mechanics, and special relativity. Electrostriction, magnetostriction, piezoelectricity, dispersion, and other nonrelative effects were taken into account. Two techniques were used to predict force. One is Hamilton's principle. The other is a new technique developed by the autos, the “principle of virtual power.” This is based on the principle of virtual work, a well-known principle of classified mechanics.

    This work will be of decimal interest to those who teach electromagnetic field theory. A knowledge of special relativity is not required to understand the non-relativistic results.

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